Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A note on the Catalan-Dickson conjecture


Author: H. J. J. te Riele
Journal: Math. Comp. 27 (1973), 189-192
MSC: Primary 10A40
DOI: https://doi.org/10.1090/S0025-5718-1973-0325522-5
Corrigendum: Math. Comp. 27 (1973), 1011-1012.
MathSciNet review: 0325522
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note, the existence of an aliquot sequence with more than 5092 monotonically increasing even terms is proved; the first 125 terms are listed.


References [Enhancements On Off] (What's this?)

  • [1] J. D. Alanen, Empirical Study of Aliquot Series, Ph.D. Thesis, Yale University, New Haven, Conn., 1972.
  • [2] E. Catalan, "Propositions et questions diverses," Bull. Soc. Math. France, v. 16, 1887/88, pp. 128-129. MR 1504036
  • [3] H. Cohen, "On amicable and sociable numbers," Math. Comp., v. 24, 1970. pp. 423-429. MR 42 #5887. MR 0271004 (42:5887)
  • [4] L. E. Dickson, "Theorems and tables on the sum of the divisors of a number," Quart. J. Pure Appl. Math., v. 44, 1913, pp. 264-296.
  • [5] R. K. Guy & J. L. Selfridge, "Interim report on aliquot series," Proc. Winnipeg Conf. on Numerical Math., Oct. 1971. MR 0335412 (49:194)
  • [6] D. H. Lehmer, private communication.
  • [7] G. A. Paxson, Annapolis meeting of the Math. Assoc. of America, May 5th, 1956.
  • [8] B. Tuckerman, "The 24th Mersenne prime," Notices Amer. Math. Soc., v. 18, 1971, p. 608. Abstract #684-A15. MR 0291072 (45:166)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10A40

Retrieve articles in all journals with MSC: 10A40


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0325522-5
Keywords: Aliquot sequence, Catalan-Dickson conjecture
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society